Question: Simplify the following expression: $\dfrac{88q^5}{72q^5}$ You can assume $q \neq 0$.
Explanation: $ \dfrac{88q^5}{72q^5} = \dfrac{88}{72} \cdot \dfrac{q^5}{q^5} $ To simplify $\frac{88}{72}$ , find the greatest common factor (GCD) of $88$ and $72$ $88 = 2 \cdot 2 \cdot 2 \cdot 11$ $72 = 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3$ $ \mbox{GCD}(88, 72) = 2 \cdot 2 \cdot 2 = 8 $ $ \dfrac{88}{72} \cdot \dfrac{q^5}{q^5} = \dfrac{8 \cdot 11}{8 \cdot 9} \cdot \dfrac{q^5}{q^5} $ $\phantom{ \dfrac{88}{72} \cdot \dfrac{5}{5}} = \dfrac{11}{9} \cdot \dfrac{q^5}{q^5} $ $ \dfrac{q^5}{q^5} = \dfrac{q \cdot q \cdot q \cdot q \cdot q}{q \cdot q \cdot q \cdot q \cdot q} = 1 $ $ \dfrac{11}{9} \cdot 1 = \dfrac{11}{9} $